Dots-And-Boxes is a well-known and widely-played combinatorial game. While the rules of play are very simple, the state space for even small games is extremely large, and finding the outcome under optimal play is correspondingly hard. In this paper we introduce a Dots-And-Boxes solver which is significantly faster than the current state-of-the-art: over an order-of-magnitude faster on several l...

We develop a rigorous theory of observation for dynamical systems in Hilbert spaces. This work generalizes the results of Ott and Yorke [8] for dynamical systems in Rn.

In this paper the notion of smooth complete semidynamical systems is studied. A relation between the rank of the derivatives of a motion at a point and at the identity of that point is deduced. A method for constructing top generalized subgroups is considered. Connected component of an identity as a top generalized normal subgroup is studied. A criterion for the connectedness of an inverse imag...

Abstract Design Theory is a mathematical theory of design based on Yoshikawa’s General Design Theory and Barwise and Seligman’s Channel Theory. Classifications is the structures of Channel theory, and they are used in Abstract Design Theory in order to formulate a scheme of design. Yoshikawa discussed design in terms of topology in General Design Theory. The aim of this paper is to show propert...

We prove that every topological space (T0-space, T1-space) can be embedded in a pseudoradial space (in a pseudoradial T0-space, T1-space). This answers the Problem 3 in [2]. We describe the smallest coreflective subcategory A of Top such that the hereditary coreflective hull of A is the whole category Top.

abstract strawberry is one of the most important fruit crops in the world. in this study, effect of different plant densities were studied on yield and fruit quality of strawberry 'selva' in greenhouse and laboratories of university college of agriculture and natural resources during 2002-2003. uniform stolens of strawberry were planted in holes of plastic column according to factorial in compl...

In this paper by definition of generalized action of generalized Lie groups (top spaces) on a manifold, the concept of stabilizer of the top spaces is introduced. We show that the stabilizer is a top space, moreover we find the tangent space of a stabilizer. By using of the quotient spaces, the dimension of some top spaces are fined.

We propose an integrated approach for solving both problems of finding the most popular k elements, and finding frequent elements in a data stream. Our technique is efficient and exact if the alphabet under consideration is small. In the more practical large alphabet case, our solution is space efficient and reports both top-k and frequent elements with tight guarantees on errors. For general d...